This paper studies the generalized Dirichlet process ( \(\mathcal{GDP}\) ) with its main properties, including moments of random weights and tail moments. We present the truncated \(\mathcal{GDP}\ as a finite mixture distribution and assess the error bounds caused by the truncation. This tactic provides more practicable stick-breaking priors in nonparametric Bayesian settings and facilitates computation. We obtain the joint density of random weights, show that the number of distinct values varies on raising the $\mathcal{GDP}$ samples, and present the impact of the precision parameter on this number. We also show that our results coincide with the Dirichlet process \((\mathcal{DP})\) .
MSC Classification: 62E15 , 60C05 , 97K60